The central theme of this program project is the development of quantitative methods, based on biological mechanism, to address important problems in cancer and AIDS. To this end, biologically-based mathematical models will be developed, together with the requisite statistical methods and computational tools for the analysis of data using these models. The usefulness of the models will be demonstrated by analyses of substantial data sets. Three research projects are proposed. 1. Stochastic Models of Carcinogenesis with Applications to Analyses of Epidemiologic and Experimental Data. In this project stochastic models of carcinogenesis will be developed for analyses of time-to-tumor data in epidemiologic and experimental studies and for analyses of intermediate lesions on the pathway to cancer in initiation-promotion experiments. 2. Risk Prediction Models for Breast and other Cancers. In this project, risk prediction models, based on the natural history of the disease and incorporating both genetic and environmental factors, will be developed for breast and other cancers 3. Quantitative methods for Modelling HIV Infection Dynamics: In this project, deterministic and stochastic models will be developed for describing interactions between HIV and the immune system during the acute and early stages of infection.